Probing the Page transition via approximate quantum error correction

TL;DR

This paper connects black hole information recovery and the Page transition to approximate quantum error correction, suggesting that the Page transition is a property of such error correction in quantum systems, enhancing understanding of black hole entropy.

Contribution

It demonstrates that the Page transition can be interpreted as a feature of approximate quantum error correction, providing a new perspective on black hole evaporation and information recovery.

Findings

Page transition is a property of approximate quantum error correction.

Black hole evaporation can be understood through the lens of quantum error correction.

Quantum systems under certain conditions exhibit phenomena similar to the Page transition.

Abstract

In recent years, there is a huge progress in understanding the black hole information problem, and the key is that the black hole entropy of radiation should be calculated by the island formula, which describes the Page curve to ensure the unitarity of black hole evaporation. In the paper, we find that the black hole evaporation interpreted by the island formula can be understood in the language of approximate quantum error correction. Furthermore, the Page transition, as a special property of the Page curve, should be understood as the property of approximate quantum error correction itself, i.e. a general class of quantum systems under certain conditions from approximate quantum error correction can also exhibit phenomenon similar to the Page transition.